You buy a 25 W lightbulb in Europe, where electricity is deliveredto homes at 23

Question

You buy a 25 W lightbulb in Europe, where electricity is deliveredto homes at 230 V. If you use the lightbulb in the United States at120 V (assume its resistance does not change), how bright will itbe relative to 25 W 120 V bulbs? Calculate how much power it willconsume.
Assume roughly that brightness is proportional to powerconsumed Honestly I'm confused about what's being asked I know P=V^2/R and R is constant but where do I go from thereif the Power is already given?? Assume roughly that brightness is proportional to powerconsumed Honestly I'm confused about what's being asked I know P=V^2/R and R is constant but where do I go from thereif the Power is already given?? Assume roughly that brightness is proportional to powerconsumed

Explanation / Answer

the intensity of the light bulbs is I1 = (P1/A1)-----------(1) and I2 = (P2/A2)------------(2) (1)/(2) (I1/I2) =[(P1/A1)/(P2/A2)] or (I1/I2) =(P1/P2) * (A2/A1) the area of the light bulb is same therefore we get
A2 = A1 or (I1/I2) =(P1/P2) * (A1/A1) =(P1/P2) =((V12/R1)/(V22/R2)) R1 = R2 or (I1/I2) =(V1/V2)2 = (230/120)2 =3.67 or I1 = 3.67 * I2 the 25 W 230 V light bulb will be 3.67 times brighter than the25 W 120 V light bulb. the resistance of the light bulb is R1= (V12/P1) =((230)2/25) = 2116 ohm the power consumed by the light bulb in united states is P2 = (V22/R2) =(V22/R1) =((120)2/2116) = 6.8 W the 25 W 230 V light bulb will be 3.67 times brighter than the25 W 120 V light bulb. the resistance of the light bulb is R1= (V12/P1) =((230)2/25) = 2116 ohm the power consumed by the light bulb in united states is P2 = (V22/R2) =(V22/R1) =((120)2/2116) = 6.8 W

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